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Simplifying 4v4 + 24v3 + 56v2 = 0 Reorder the terms: 56v2 + 24v3 + 4v4 = 0 Solving 56v2 + 24v3 + 4v4 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4v2'. 4v2(14 + 6v + v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'v2' equal to zero and attempt to solve: Simplifying v2 = 0 Solving v2 = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v2 = 0 Take the square root of each side: v = {0}Subproblem 2
Set the factor '(14 + 6v + v2)' equal to zero and attempt to solve: Simplifying 14 + 6v + v2 = 0 Solving 14 + 6v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 6v + -14 + v2 = 0 + -14 Reorder the terms: 14 + -14 + 6v + v2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 6v + v2 = 0 + -14 6v + v2 = 0 + -14 Combine like terms: 0 + -14 = -14 6v + v2 = -14 The v term is 6v. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6v + 9 + v2 = -14 + 9 Reorder the terms: 9 + 6v + v2 = -14 + 9 Combine like terms: -14 + 9 = -5 9 + 6v + v2 = -5 Factor a perfect square on the left side: (v + 3)(v + 3) = -5 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
v = {0}
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